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Find the derivative of the given function 4. g(x) = (4 – 9x²)3 5. h(x) x+5 = x2-9, 6. A(x) = v3x3 + 4x – 1

Find the derivative of the given function 4. g(x) = (4 – 9x²)3 5. h(x) x+5 = x2-9, 6. A(x) = v3x3 + 4x – 1

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### Calculus: Derivatives #### Problem Set Find the derivative of the given function: 4. \( g(x) = (4 - 9x^2)^3 \) 5. \( h(x) = \left( \frac{x+5}{x^2 - 9} \right)^3 \) 6. \( A(x) = \sqrt{3x^3 + 4x - 1} \) #### Explanation - **Function \( g(x) \)** involves a polynomial raised to a power, suggesting the use of the chain rule for differentiation. - **Function \( h(x) \)** is a rational function raised to a power, which will also require the chain rule along with the quotient rule. - **Function \( A(x) \)** involves a square root, indicating that it may be rewritten using an exponent of \( \frac{1}{2} \) for differentiation purposes using the chain rule.
Transcribed Image Text:### Calculus: Derivatives #### Problem Set Find the derivative of the given function: 4. \( g(x) = (4 - 9x^2)^3 \) 5. \( h(x) = \left( \frac{x+5}{x^2 - 9} \right)^3 \) 6. \( A(x) = \sqrt{3x^3 + 4x - 1} \) #### Explanation - **Function \( g(x) \)** involves a polynomial raised to a power, suggesting the use of the chain rule for differentiation. - **Function \( h(x) \)** is a rational function raised to a power, which will also require the chain rule along with the quotient rule. - **Function \( A(x) \)** involves a square root, indicating that it may be rewritten using an exponent of \( \frac{1}{2} \) for differentiation purposes using the chain rule.
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